Current fleet assignment models allow no variability in the scheduled departure time of flights even though exploiting this variability can result in more flight connection opportunities and a more cost effective fleet assignment. We present a generalized model that exploits this variability, simultaneously assigning aircraft types to flights and scheduling flight departures.We model this problem as a simple variant to current fleet assignment models, assigning a time window to each flight and then discretizing each window, allowing the model to select the departure time. As problem size can become formidable, much larger than current fleet assignment models, we develop two algorithmic approaches for solving the model. Our direct solution approach is good for speed and simplicity, while our iterative technique minimizes memory usage.Using data from a major U.S. airline. we show that our model can solve real, large-scale problems, and we evaluate the effects of schedule flexibility. In every test scenario, the model produces a fleet assignment with significantly lower costs than the basic model, and in a separate analysis, the model is used to tighten the schedule, potentially saving aircraft.